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Holostar thermodynamics

Michael Petri
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Abstract

The holostar is an exact solution of the Einstein field equations with a singularity free interior matter-density rho = 1 / (8 pi r^2) and a boundary membrane consisting out of tangential pressure. Although the interior matter has on overall string equation of state, part of the matter can be interpreted in terms of particles. A simple thermodynamic model is presented, treating the matter as an ideal gas of (ultrarelativistic) fermions and bosons. The number of ultra-relativistic particles within a holostar is proportional its surface-area, indicating that the holographic principle is valid in classical GR for self gravitating objects of any size. Using the grand canonical formalism we show, that the interior temperature is given by T \propto / \sqrt{r}. With a surface redshift z \propto \sqrt{r} the holostar's temperature at infinity is equal to the Hawking result, up to a constant factor. The factor depends on the number of particle degrees of freedom at the Planck energy, which is estimated as f ~ 7000. The holostar's total thermodynamic entropy is proportional to the area of its boundary membrane. The ultra-relativistic fermions in the interior space-time must acquire a non-zero chemical potential, which acts as a natural source for a profound matter-antimatter asymmetry at high temperatures. The local values of the interior temperature and matter-density are related to the holostar's temperature at infinity, enabling a "measurement" of the Hawking temperature from the interior space-time. Using the experimental values for the CMBR-temperature and the total matter-density of the universe determined by WMAP the Hawking result is verified to an accuracy of 1%.ior particles. Some properties expected from a rotating holostar are discussed briefly.

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Michael Petri. 2004-05-02. Holostar thermodynamics. https://arxiv.org/abs/gr-qc/0306067

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